What will happen if some global governance regimes try to assert their authority over other regimes? This is from a paper by Lukasz Gruszczynski:
The current language of the [Framework Convention on Tobacco Control] does not provide any exclusion clause that would prevent the recourse to other international dispute settlement systems once its mechanism has been activated. Nevertheless, one may not exclude, considering the stance taken by some FCTC parties during the COP meetings (as well as position advocated by many non-governmental organisations in the field of public health), that the convention can be amended in the future. Such an amendment may preclude a recourse to any other dispute settlement systems once a case is in the dispute settlement process under the FCTC. It may also provide an option for the parties to choose between two different systems that are available in a particular situation (a kind of fork-in-the-road provision found in Art. 2005.6 NAFTA). Without determining the consequences of such clauses for other trade and investment dispute settlement systems, it seems clear that they will neither affect the jurisdiction of WTO panels / the Appellate Body nor will they make a case inadmissible (aside from the problem of conflict of jurisdictions – see my remarks above).
I suspect that a flexible system which allows multiple dispute settlement systems to review related issues will work just fine, and there is no need for exclusion clauses of this sort. My sense is that dispute panels in one system will be able to take into account rulings by panels in other systems without too much conflict or confusion.